Pascal and a triangular billiard

Abstract

Is any triangle fit to be a billiard orbit in some ellipse? Is it unique? Can we draw it as a point-conic? We show that this is always the case and provide a synthetic proof leading to a new construction for both the billiard and its caustic. The link between the billiard, incircle, and Euler circle emerges almost naturally. Neat geometric ties between the caustic and exinscribed circles are also brought to light.